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We study the thermal Markovian diffusion of tracer particles in a 2D mediumwith spatially-varying diffusivity $D(r)$, mimicking recently measured,heterogeneous maps of the apparent diffusion coefficient in biological cells.For this heterogeneous diffusion process (HDP) we analyse the mean squareddisplacement (MSD) of the tracer particles, the time averaged MSD, the spatialprobability density function, and the first passage time dynamics from the cellboundary to the nucleus. Moreover we examine the non-ergodic properties of thisprocess which are important for the correct physical interpretation of timeaverages of observables obtained from single particle tracking experiments.From extensive computer simulations of the 2D stochastic Langevin equation wepresent an in-depth study of this HDP. In particular, we find that the MSDsalong the radial and azimuthal directions in a circular domain obey anomalousand Brownian scaling, respectively. We demonstrate that the time averaged MSDstays linear as a function of the lag time and the system thus reveals a weakergodicity breaking. Our results will enable one to rationalise the diffusivemotion of larger tracer particles such as viruses or submicron beads inbiological cells.

Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity